Plasma Surface Interactions in LaB₆ Hollow Cathodes with Internal Xe Gas Discharge

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Plasma Surface Interactions in LaB

6

Hollow

Cathodes with Internal Xe Gas Discharge

Thesis by:

Pedro Pablo Guerrero Vela

In Partial Fulfillment of the Requirements for the Degree of

Doctor

of

Philosophy

in

Space

Engineering

CALIFORNIA INSTITUTE OF TECHNOLOGY

Pasadena, California

2019

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Pedro Pablo Guerrero Vela ORCID: 0000-0001-5766-2038

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ACKNOWLEDGEMENTS

First and foremost, I would like to express my deepest gratitude to my advisor at JPL Dr. James E. Polk for giving me the opportunity to work in the exciting field of electric propulsion technologies and for his continuous support and guidance throughout the entirety of my PhD work.

I would also like to thank my Caltech advisors Prof. Joanna M. Austin and Prof. Daniel I. Meiron for their advice and guidance, Prof. Dale I. Pullin and Prof. Joseph E. Shepherd for their valuable feedback as part of my candidacy and thesis defense committees, and Prof. Michael Ortiz and Prof. Pilar Ariza for providing me the life changing opportunity to be part of the Caltech community.

Given the multidisciplinary nature of electric propulsion technologies, collaborations with scientists from other fields have been essential to obtain fruitful results for this work. I am thankful to the following individuals who assisted me in this project and/or kindly helped by providing me with their expertise: Prof. Katherine Faber, Prof. Rosa Carmina Monreal, Prof. Michael Trenary, Prof. William A. Goddard, Prof. Kimberly A. See, Dr. Chi Ma, Benjamin Herren, Dr. Matthias Richer, Ellen Yan and Dr. Channing C. Ahn.

A special mention goes to the JPL staff without whom this work and my experience would not have been the same: Dr. Dan Goebel, Dr. Yiangos Mikellides, Dr. Alejandro Lopez Ortega, Dr. Lee Johnson, Dr. Richard Hofer, Dr. John Brophy, Dr. Ira Katz, Dr. Colleen Marrese-Reading, Dr. Robert Lobbia, Dr. Vernon Chaplin, Dr. Ryan Conversano, Giulia Becatti, Ray Swindlehurst and Nowell Niblett.

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literature for my research.

I also acknowledge the financial support of the joint NASA-GRC and JPL development of the HERMeS Hall thruster by NASA’s Space Technology Mission Directorate through the Solar Electric Propulsion Technology Demonstration Mission project.

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ABSTRACT

The ultimate goals of space vehicles are to move faster, further, and more reliably in the space environment. Electric propulsion (EP) has proven to be a necessary technology in the exploration of our solar system ever since its working principle was empirically tested in space in 1964. Thanks to the high exhaust velocities of ionized propellant gases, EP enables efficient utilization of the limited supply of propellant aboard spacecrafts. This technology has opened the possibility of long distance autonomous space missions.

EP devices require electron sources to ionize the propellant gas and to neutralize charges that are leaving the spacecraft. In modern EP thrusters, this is achieved by the use of hollow cathodes – complex devices that employ low work function materials to emit electrons. Hollow cathodes using polycrystalline LaB6 inserts

are attractive candidates for long duration EP based space missions. However, the physics behind LaB6 hollow cathode operation has not been studied in detail,

which limits the possibility of their optimization. This work presents an integrated experimental and computational approach to investigate LaB6 hollow cathode

thermal behaviour and the interplay between LaB6 insert surface chemistry and

xenon plasma.

Our investigation of the thermal behaviour of LaB6 cathodes led to the

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work function (0.42 eV) compared to previously reported baseline values, which is of paramount importance for EP thruster efficiency and operational lifetimes. Second, simulations suggested that the interaction between xenon low energy ions (< 50 eV) and the LaB6 surface occurs following a two step neutralization

mechanism. The predicted work function reduction was experimentally confirmed by photoemission spectroscopy. Furthermore, using a combination of crystallographic analysis, scanning electron microscopy and profilometry, we demonstrated that work function reduction is caused by the creation of a crystallographic texture at the LaB6 surface upon interaction with Xe plasma. In

addition, we postulated the existence of a work function enhancing mechanism of secondary importance, which can be explained by forced cationic termination of plasma exposed crystals.

Our results revealed the unexpected phenomenon of work function reduction upon plasma exposure of LaB6. These findings suggest that LaB6 hollow cathodes

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PUBLISHED CONTENT AND CONTRIBUTIONS

Guerrero, P., Polk, J.E., et al. (2017). “Work function reduction in lanthanum hexaboride hollow cathodes operated in gas discharges". In: 35t h International Electric Propulsion Conference. (Atlanta, GA, USA). IEPC-2017-399 URL:

http://erps.spacegrant.org/IEPC_2017/IEPC_2017_399.pdf . Journal paper in preparation.

P.G. contributed to the conception of this work, design and development of the experimental setup, execution of the experiments, data analysis, writing of the manuscript, and preparation of figures.

Guerrero, P., Mikellides, I.G., et al. (2018). “Hollow cathode thermal modelling and self-consistent plasma solution: work function evaluation for a LaB6 cathode.".

In: 53r d AIAA/SAE/ASEE Joint Propulsion Conference. (Cincinnati, OH, USA). DOI: 10.2514/6.2018-4511

Guerrero, P., Mikellides, I.G., et al. (2019). “Hollow cathode thermal modelling and self-consistent plasma solution: two step neutralization modelling.". In: 36t h International Electric Propulsion Conference. (Vienna, Austria). Journal paper in preparation.

Guerrero, P., Polk, J.E., et al. (2019). “LaB6 hollow cathode work function

enhancement: insight into the chemical processes.". In: 36t h International Electric Propulsion Conference. (Vienna, Austria). Journal paper in preparation.

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Mikellides, I.G., Goebel, D.M., Jorns, B.A., Polk, J.E., Guerrero, P. (2015). “Numerical Simulations of the Partially Ionized Gas in a 100-A LaB6 Hollow

Cathode". In: IEEE Transactions on Plasma Science 1 (43), pp. 173-184. DOI: 10.1109/TPS.2014.2320876

P.G. contributed to the design and development of the temperature measurement experimental setup, execution of the experiments and data analysis.

Polk, J.E., Goebel, D.M., Guerrero, P. (2015). “Thermal Characteristics of a Lanthanum Hexaboride Hollow Cathode". In: 34t h International Electric Propulsion Conference. (Kobe, Japan). IEPC-2015-44 URL:http://erps.spacegrant.

org/uploads/images/2015Presentations/IEPC-2015-44_ISTS-2015-b-44.pdf P.G. contributed to the design and development of the temperature measurement experimental setup, execution of the experiments and data analysis.

Yanes, N.J., Guerrero, P., Friss, A.J., Polk, J.E., Jorns, B.A., Austin, J. (2016). “Ion Acoustic Turbulence and Ion Energy Measurements in the Plume

of the HERMeS Thruster Hollow Cathode.". In: 52nd AIAA/SAE/ASEE Joint Propulsion Conference. (Salt Lake City, UT, USA). DOI: 10.2514/6.2016-5028 P.G. contributed to the conception of this work, design and development of the experimental setup and execution of the experiments.

Mikellides, I.G., Guerrero, P., Ortega, A.L., Goebel, D.M., Polk, J.E. (2018). “Spot-to-plume Mode Transition Investigations in the HERMeS Hollow Cathode Discharge Using Coupled 2-D Axisymmetric Plasma-Thermal Simulations". In: 53r d AIAA/SAE/ASEE Joint Propulsion Conference. (Cincinnati, OH, USA). DOI: 10.2514/6.2018-4722

P.G. contributed to the conception of this work.

Polk, J.E., Lobbia, R., Barriault, A., Guerrero, P., Mikellides, I.G., Ortega, A.L. (2017). “Inner Front Pole Cover Erosion in the 12.5 kW HERMeS Hall Thruster

Over a Range of Operating Conditions". In: 35t h International Electric Propulsion Conference. (Atlanta, GA, USA). IEPC-2017-409 URL: https://iepc2017.org/

sites/default/files/speaker-papers/iepc2017sla_measurements_final_0.

pdf .

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cathode experimental setup and execution of the experiments.

Becatti, G., Goebel, D.M., Polk, J.E.,Guerrero, P. (2017). “Life Evaluation of a Lanthanum Hexaboride Hollow Cathode". In: Journal of Propulsion and Power 4 (34),pp. 893-900. DOI: 10.2514/1.B36659

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LIST OF ILLUSTRATIONS

Number Page

1.1 Implications of the rocket equation . . . 3

1.2 LaB6 crystal structure. . . 7

1.3 LaB6 phase diagram. . . 8

1.4 Work function of different LaB6 crystal faces computed from DFT simulations. . . 10

2.1 LaB6 hollow cathode schematic . . . 24

2.2 Insert finite element model with three thermocouples wells . . . 25

2.3 Thermal transient for a new insert with the nominal orifice . . . . 27

2.4 Thermal transient with the nominal orifice after exposing the cathode to the atmosphere for several hours . . . 28

2.5 Thermal transient associated with hot reignition . . . 29

2.6 Thermal transient evolution with discharge current . . . 30

2.7 Abnormal thermal transient after a hot reignition . . . 31

2.8 Detail of the contaminant deposited on the inside of the insert . . . 32

2.9 Steady state temperature distribution for each cathode configuration and each thermocouple . . . 33

2.10 Temperature profiles approximated by a second degree polynomial fit to the thermocouple data for each operating condition . . . 35

2.11 Cathode effective emitting area sensitivity analysis . . . 36

2.12 Estimated work function with temperature data . . . 39

2.13 JD(φopt) − JD,measured, zero return current and φSchottky = 0eV . . 40

2.14 Work function as a function of depth measured at three different positions along the insert inner surface . . . 42

2.15 Insert piece inside the KRATOS Ultra XPS at Caltech . . . 42

2.16 Carbon atomic abundance on the insert . . . 43

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2.18 OrCa2D simulation results for the plasma potential along the cathode centerline . . . 48 2.19 Thermal transient and inferred work function for a new insert . . . . 51 2.20 Thermal heat fluxes along the insert of the cathode . . . 54 2.21 Spring loaded thermocouple assembly . . . 56 3.1 Thermionic emission sensitivity analysis for Richardson-Dushman law 64 3.2 Self-consistent platform overview . . . 69 3.3 Temperature distribution created with COMSOL (example) . . . . 70 3.4 Ta total hemispherical emissivity . . . 71 3.5 Cathode geometry . . . 72 3.6 Axisymmetric model of the hollow cathode . . . 72 3.7 Dependence of the maximum temperature of the insert surface with

the total number of elements in the Comsol thermal model . . . 74 3.8 Dependence of the maximum temperature of the insert surface with

the number of azimuthal sectors used in the COMSOL thermal model 75 3.9 Dependence of the maximum temperature of the insert surface with

the radiation resolution used in the Comsol thermal model . . . 76 3.10 Representation of the cathode thermal model, plasma and surfaces

at the interface . . . 77 3.11 Location where the thermocouples were installed . . . 78 3.12 COMSOL thermal model validation results . . . 79 3.13 Schematic of the computational domain used in the OrCa2D simulations 80 3.14 OrCa2D numerical simulation domain . . . 81 3.15 Steady-state solution for the plasma potential, electron temperature

and neutral gas density . . . 84 3.16 Comparison of a LaB6 hollow cathode operating at 100 A and 12

sccm with a BaO cathode operating at 13.3 A and 3.7 sccm. OrCa2D simulation results. . . 86 3.17 Comparison of the electron number densities along the centerline of

the two cathodes between theory and experiment. . . 87 3.18 Comparison of the plasma potential and electron temperature along

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3.19 EAC as a function of ion-surface mass ratio and ion energy. . . 90

3.20 Evolution of the temperature input to OrCa2D and output from COMSOL . . . 94

3.21 Converged temperature results for the baseline thermal model. . . 95

3.22 COMSOL thermal model validation results . . . 97

3.23 Converged temperature results, thermal model sensitivity analysis 98 3.24 Converged temperature results, sensitivity analysis forVK . . . 99

3.25 Converged temperature results, sensitivity analysis for EAC . . . . 100

3.26 Work function profiles studied in this work . . . 101

3.27 Converged temperature results, sensitivity analysis for work function distributions . . . 102

3.28 Converged temperature results, sensitivity analysis for EAC and neutralization model . . . 103

3.29 Contribution of the Schottky effect for the final self consistent solutions.105 4.1 Modified insert geometry used in this study . . . 118

4.2 Vacuum chamber used in the experiment . . . 119

4.3 Cathode assembly inside vacuum chamber . . . 120

4.4 Test sample (part A) . . . 121

4.5 UPS spectra for the LaB6 test article after plasma exposure. . . 123

4.6 Thermal transient for a new, two part insert . . . 127

4.7 Thermal transient during shut down . . . 127

4.8 Part 1: cathode operational parameters measured during 50 hr test 128 4.9 Part 2: cathode operational parameters measured during 50 hr test 128 4.10 Test sample (part B) after the 50 hr test . . . 129

4.11 On the left, SEM image collected from a sample after manufacturing. On the right, SEM pictures from the test sample after exposure to plasma . . . 130

4.12 Surface profiles acquired before plasma exposure . . . 131

4.13 Surface profiles acquired after plasma exposure . . . 132

4.14 Work function measurements acquired with UPS . . . 134

4.15 Test sample XRD spectra results, comparison with LaB4 . . . 135

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LIST OF TABLES

Number Page

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NOMENCLATURE

§§§

¯

z Dimensional coordinate along centerline of the cathode

Û

mXe Xenon mass flow rate

φ Work function

φSchottky Modification of the work function due to the Schottky effect

ε Total hemispherical emissivity

D Richardson-Dushman law constant

e Electron charge

JD Net discharge current

jther Thermionic emission density

kB Boltzmann constant

T Temperature

Tinsert(z) Temperature distribution along the hollow cathode insert

VD Discharge voltage

VK Keeper voltage

DFT Density functional theory

EBSD Electron back scatter diffraction

EP Electric propulsion

HIP Hot isostatic pressing

IAT Ion acoustic turbulence

MPD Magnetoplasmadynamic

SEM Scanning electron microscope

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C h a p t e r 1

INTRODUCTION

Exploration beyond the boundaries of Earth has captured human imagination since ancient times. With billions of galaxies in the observable universe, space offers a wealth of discoveries, opportunities, and resources. Technological advances in the 20th _{century have allowed humans for the first time in history to pioneer}

space exploration. However, in order to travel further in space, more progress has to be made in propulsion technology.

In order to cover the vast distances between objects in space, it is necessary to use a propulsion system that efficiently utilises the limited supply of propellant aboard the spacecraft while maintaining reasonable flight times (human time scales). Efficiency, in this context, means the maximal utilization of the propellant mass available for thrust purposes. The energetic requirements necessary to complete a space mission are specified by the quantity Delta-V. Therefore, a propulsion

system is more efficient when it can obtain a given Delta-V with less propellant.

The ideal rocket equation, first derived by mathematician William Moore in 1813, describes the motion of vehicles in space (see Fig. 1.1). It shows that the propellant has to be ejected from the vehicle at the highest possible speed in order to optimize its use.

Conventional chemical propulsion is limited by the amount of energy released in the combustion reaction. The maximum exhaust velocities that can be achieved with known fuels and oxidizers are only a few km/s. Therefore, this technology is considered “energy-limited”. However, given that propellants are their own energy source, the power supplied to the propellant is independent of the mass of the vehicle. This enables very high thrust-to-weight ratios to be attained.

In order to enable space missions with high Delta-V, such as the Dawn mission

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0 5 10 15 0

20 40 60 80

100 Implications of the rocket equation

v = 1 km/se ve

= 2 km/s

v_e = 4 km/s

ve = 6 km/s

v_e = 10 km/s

v_e = 15 km/s

v_e = 30 km/s

v_e = 50 km/s

v

e = 100 km/s

v_e: exhaust velocity

Chemical propulsion limit

Figure 1.1: Implications of the rocket equation. mp is the propellant mass, m0 is

the initial mass of the vehicle.

missions in the first half of the 20th _{century and later demonstrated in space in}

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1.1. Electric propulsion overview P. Guerrero

component lifetime is one of the most important parameters to take into account when designing electric thrusters.

1.1 Electric propulsion overview

In EP, propellant gases are accelerated by direct electric heating and/or electromagnetic body forces. Conceptually, EP is divided into three categories – electrothermal, electrostatic and electromagnetic propulsion systems. This division is based on the different physical mechanisms used to accelerate the propellant. The most widely used electric thrusters are electrothermal (arcjets and resistojets). Pulsed magnetoplasmadynamic (MPD) thrusters have only flown on a few technology demonstrator missions and are still in the laboratory development phase. Hall-effect thrusters and gridded ion thrusters are electromagnetic propulsion systems that have been under development since the 1960s. Today, increasing numbers of commercial companies are developing Hall and ion thrusters, and only these two have been used for deep space missions.

In order to produce thrust, most EP devices need to ionize the propellant gas and accelerate the resultant ions by applying an electric field or a combination of electric and magnetic field. The ions are then ejected at very high speeds out of the spacecraft, forming the thruster plume. As the ions leave the thruster, charges accumulate in the space vehicle. These charges need to be neutralized, otherwise the spacecraft would continuously charge and attract the ions back with increasing strength, ultimately rendering zero thrust. Cathodes are fundamental components of these EP systems. First, they provide the electrons necessary to ionize the propellant, and second they are responsible for neutralizing the plume. Therefore, advancing cathode technologies are of central interest for the research community in EP and the motivation for this work.

1.2 Review of cathode technologies

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electrons thermionically. Thermionic emission for a given material is determined by the amount of energy required to extract electrons – a property termed “work function.” Due to the relatively high work function of these metals (e.g. 4.55 eV for tungsten), filament cathodes required working temperatures of up to 2600 K [4]. These high operating temperatures however led to rapid evaporation of the cathode material, limiting filament cathode lifetimes. Additionally, in order to reach the required emission temperature, the filaments were directly heated by passing current through them. This was achieved by mounting the filament in an open configuration which exposed the emitting material to high energy ions, thus further impacting the cathode lifetime because of sputtering – a wear mechanism based on the ejection of material due to the interaction of its surface with high energy particles. Collectively, the high operating temperature and sputtering permitted only hundreds of hours of available operation for this primitive cathode design.

To address the short lifetime of filament cathodes, the hollow cathode design was created. In this design electrons are emitted by a so-called emitter, which is enclosed and protected by an orifice plate and a keeper (see section 2.2). Electrons flow from the emitter to the thruster discharge or plume with a relatively low potential drop because a high conductivity plasma is created inside and outside the cathode. The cathode plasma extends outwards until it merges with the thruster plasma, thus creating a suitable medium for charges to move between cathode and thruster. The closed hollow cathode architecture presents several key improvements with respect to the primitive filament cathode approach. First, it creates the cathode plasma efficiently, which is important for electron transport. Second, continuous emission is only possible thanks to a carefully designed thermal architecture coupled with low work function emitters, which makes them energetically efficient and improves the thruster energy demand as a whole. Finally, hollow cathodes are very compact because their emission is not controlled by space-charge limitations. This characteristic is highly desirable as it enables very high current densities to be extracted from the cathode with yet small overall size.

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1.3. Properties of LaB6 P. Guerrero

allow abundant electron emission per gram of material evaporated, thereby extending the lifetime of the cathode. Thus, the most important feature for a cathode emitter is to have low work function. Furthermore, a key characteristic of hollow cathodes is that they are self-heating devices, i.e. the emitting surfaces of the cathode are heated by the internal plasma and do not require an external heat source. From a practical standpoint, this can only be achieved with materials that require relatively low operating temperatures to emit electrons. Thus, low work function materials also enable the self-heating property of hollow cathodes. The ideal emitter material also needs to be resistant to contamination from impurities in the propellant gas or feed system. Emitters whose efficiency is influenced by small amounts of contaminants in the propellant gas are not desirable.

Hollow cathodes can be grouped into two categories based on the technology of the emitter material: composite and bulk emitters, also known as dispenser and crystalline cathodes respectively. Composite emitters are based on low work function surfaces created with electronegative adatoms deposited on an appropriate substrate. The adatoms form a dipole at the surface which reduces the energy required for electrons to be emitted thermionically. Composite cathodes use compounds with extremely low work functions. One of the best known composite cathodes is the BaO-W cathode, widely used in space applications. However, a major disadvantage of these systems is the limited amount of substance that can be held by the substrate. Bulk cathodes use single crystals or polycrystalline materials that exhibit low work function. The main advantage of crystalline cathodes is the abundance of material available for emission. As the surface of the emitter evaporates away, the newly exposed surface exhibits the same emission profile. The most widely used material in bulk cathode technologies is polycrystalline LaB6.

1.3 Properties of LaB

6

Boron-based materials have been studied since the 1950s due to their excellent chemical bonding, crystal structure and phonon and electron conduction properties [5]. The first experimental use of LaB6 as an effective thermionic emitter is commonly

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2.66 eV. Many uses for LaB6 as a cathode material have been found since, including

but not limited to X-ray sources, electron beam pumped lasers, thermionic energy converters, ion beam sources, halogen atomic beam detectors, negative ion surface ionizers, scanning electron microscopes, transmission microscopes, electron probes, scanning Auger systems and electron lithography systems.

LaB6 is a refractory ceramic material characterized by high melting point

(2988 K [7]), strength, chemical and thermal stability, low vapor pressure, electronic work function, resistivity, thermal expansion coefficient, and high current and voltage capabilities, among other properties. The crystal structure of LaB6 is

simple cubic with octahedral space group P m3m and central La cations (Fig. 1.2).

The lattice parameter (number 1 in Fig. 1.2) is 4.1569 Å, the intraoctahedral parameter is 1.766 Å (2) and the interoctahedral parameter is 1.659 Å (3) [8]. The phase diagram can be found in Fig. 1.3.

Figure 1.2: LaB6 crystal structure. Image produced with VESTA [9] using data

from [10].

The excellent thermionic behavior of LaB6 is due to its surface structure,

which in turn derives from the bulk structure. Per unit cell, LaB6 contains one La

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1.3. Properties of LaB6 P. Guerrero

Figure 1.3: LaB6 phase diagram. Reprinted with permission from the copyright

holder [11]. Adapted.

intraoctahedral covalent bonds. Each B6 unit is bonded to adjacent cells B6 units

covalently as well. This boron network is electron deficient, a situation that gets resolved with the transfer of 2 electrons per unit cell from the La atoms [12, 13]. The third electron of the trivalent metal atoms enters into a metallic conduction band that bonds La atoms between each other metallically. LaB6 contains covalent

B-B bonds, ionic La-B bonds and metallic La-La bonds [14] and this peculiar network of bonds is responsible for the unique set of macroscopic properties of the material.

Polycrystalline LaB6has an estimated work function of 2.66 eV [6]. Polycrystalline

materials have complex surfaces composed of different crystals, with individual crystals exhibiting different work functions. In the case of LaB6, the work functions

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chemical constituents. The composition of the topmost atomic layer is an important determinant of the work function. In the case of LaB6the crystals can be terminated

in the La or B atomic layer. The electronegativities of La and B on the Pauling scale are 1.1 and 2.04 respectively. Therefore, La terminations are cationic and B terminations are anionic. Depending on the crystal, this termination naturally occurs in one or the other [16]. Theoretical studies have established that LaB6

crystals terminating in La have a significantly lower work function compared to those terminating in B [17]. Relaxation of the lattice near the surface is another effect to take into account when computing work function. The increase in the interatomic distance between the constituent elements affects the electron density distribution at the surface and hence the work function.

Given the sensitivity of work function to the surface state, it is unsurprising that adsorbed chemicals can affect either positively or negatively the thermionic behavior of LaB6. Chemicals known to affect emission negatively include O2, H2O,

CO and carbon, and so are considered “poisons” for LaB6. Cesium is the best

known work function enhancer for LaB6, either by itself or in combination with

oxygen. Values as low as 1.35 eV for cesium coadsorbed with oxygen in the (100) LaB6 face have been reported [18].

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1.4. Research objectives P. Guerrero

(100) (110) (111) (112)

1 2 3 4 5 6

Figure 1.4: Work function of different LaB6 crystal faces computed from DFT

simulations. Data in blue is from [20]. Data in red is from [17]. Polycrystalline value is from [6]. Known natural terminations are underlined [16].

1.4 Research objectives

The main focus of this work is to characterise and understand the processes involved in establishing the working temperature of the electron emitter in a LaB6

hollow cathode fed with xenon gas. The main research goals are:

1. Characterization of the cathode insert temperature when operated with an internal gas discharge.

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3. Determination of the physical phenomena responsible for the temperature distribution of the cathode.

LaB6has been extensively studied now for almost 70 years in different fields [16].

While these studies revealed many aspects of its structure and behavior in different contexts, none of them addresses how it is affected by plasma. Most of the studies that focus on the emission properties of LaB6 are concerned with emission in

vacuum. To our knowledge, no study has focused on the interaction between low energy (< 100 eV) noble gas ions and polycrystalline LaB6 surfaces. This is the

environment that exists inside a hollow cathode with a polycrystalline LaB6 insert

fed with noble gas.

Given the dependence of EP thrusters on cathodes for their operation, the lifetime of EP thrusters can be determined by their cathode lifetime. In the hollow cathode configuration, one of the main processes that determine lifetime is the evaporation of the emitter material, which is caused by the working temperature of the emitter. The emitting surface temperature is established by thermionic emission, which in turn depends on the work function of the material. The work function of the emitter is a material property that depends on the chemical structure of the material at the surface and therefore, it can be influenced by any process that affects the surface. In the complex hollow cathode configuration, several processes can affect the surface of the emitter. One of these processes is the redeposition of evaporated chemicals from the insert that can interact with the plasma and be recycled back to the emitting surface, changing its composition. In addition, the plasma can directly interact with the surface of the emitter and affect its thermionic properties by modifying its crystallographic structure.

1.5 Thesis outline and summary

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1.5. Thesis outline and summary P. Guerrero

cathode. Results from this work served as a foundation for the development of a multidisciplinary simulation methodology for operating cathodes described in Chapter 3. In Chapter 2 we also hypothesise the possible chemical mechanisms that could explain the empirical observations. Chapter 4 presents a comprehensive study of the chemical evolution of plasma exposed LaB6 cathode surface that sheds

light on the physical basis of the cathode thermal behavior.

In order to understand the interaction between the cathode plasma and the polycrystalline LaB6 emitter surface, we developed a state-of-the-art experimental

setup consisting of a stand-alone instrumented hollow cathode placed inside a vacuum chamber capable of unattended operation. This configuration allows down to 10−5 Torr of high vacuum, which closely approximates the conditions that the cathode experiences when it runs in thrusters. Further, we developed a data acquisition system to capture all relevant parameters used for cathode diagnostics with one-second time resolution. Using this system, we discovered a thermal transient behavior of the cathode for which there was no previous evidence or explanation. Specifically, we observed that the temperature of the insert drops over the first few tenths of hours. This temperature drop is consistent with an approximately 0.4 eV decrease in the work function of the electron emitter (Chapter 2).

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The plasma structure is established by the temperature of the insert, its work function, and other effects that appear when plasma is created and interacts with the emitter surface, i.e., return current of electrons and ions, and the Schottky effect (lowering of the effective work function due to the presence of the plasma electric field on the emitting surface).

We attribute the temperature drop to a work function reduction produced by the interaction between the cathode plasma and the insert. To uncover the precise work function reduction, we developed a computational platform where all three physical effects – plasma, thermal and chemical – are simultaneously studied. This self-consistent cathode modelling approach is described in Chapter 3. A thermal model of the entire cathode was created and validated experimentally for this work. We use the plasma solver OrCa2D to simulate the distribution of electrons and ions inside the cathode [21, 22, 23, 24, 25, 26, 4]. At the interface between these two models, we compute the heat fluxes that will ultimately heat the cathode structure and establish its temperature. At this step we defined the effect of the energy accommodation coefficient and neutralization model. The platform requires the input of the experimentally measured discharge current and voltage, keeper voltage, and xenon mass flow rate to specify the boundary conditions. We use an initial plasma structure to start the simulation. This plasma structure is created using a combination of work function and temperature distribution that produces a viable numerical solution while satisfying the boundary conditions. With the plasma distribution we then compute the heat fluxes that will produce a temperature distribution once input into the thermal model. The model then outputs the temperature distribution of the cathode. If the temperature distribution of the insert does not match the one previously used to create the plasma structure, a new temperature distribution is input into the plasma solver. This new temperature distribution is closer to the one output by the thermal model. This cyclic simulation process continues until the temperature distribution produced by the thermal model is the same as the one input into the plasma solver in the previous iteration.

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1.5. Thesis outline and summary P. Guerrero

system was found. However, upon initial attempts, the simulated temperature distribution did not agree with our temperature measurements. We then studied the effect of the energy accommodation coefficient and a two-step neutralization mechanism on the self-consistent solution. The energy accommodation coefficient (EAC) is primarily influenced by the mass ratio of the ions and the atoms at the surface. For the Xe–LaB6 system, a value no less than 80% is expected. With that

EAC value no agreement with experimentally measured temperatures was found. However, we found that incorporating a two-step neutralization mechanism yields agreement with experimental measurements. This mechanism could also govern the neutralization process in other cathode technologies where low work function emitters are employed. This approach constitutes the first successful attempt to simulate a LaB6 hollow cathode with 2D axisymmetric models for the plasma and

heat transfer to the cathode that are self-consistently coupled.

Finally, we sought to understand the underlying chemical basis of the observed work function reduction upon exposure to plasma (Chapter 4). To this end, we investigated the chemical, crystallographic and morphological changes of the cathode emitting surface after it is exposed to the cathode internal plasma. Since crystallographic analyses require flat surfaces for optimal performance, we designed and fabricated a new two-part emitter geometry with a flat portion of surface.

In order to characterise the effect of plasma on the morphology evolution of the surface, we employed scanning electron microscopy (SEM). In SEM, accelerated electrons are forced to collide against a surface. When the electrons interact with the sample, they are decelerated by inelastic collisions, producing a variety of signals. One of these signals is the secondary electron emission, which is used to produce SEM images. We further used a stylus profilometer to quantify the effect of plasma on the topology evolution of the surface. Stylus profilometers measure the surface profile of a sample by physically moving the tip of a probe along the sample surface.

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technique which provides both elemental and chemical state information on virtually any material. XPS is similar to UPS except that it uses X-rays rather than ultraviolet light to excite electrons. X-rays penetrate deeper into the materials and therefore electrons from core levels can be excited. UPS and XPS can be used to directly measure the material work function.

Finally, we employed two complementary diffraction methods – electron backscattering diffraction (EBSD) and X-ray diffraction (XRD) – to identify different crystallographic phases and explore the evolution of the relative exposed crystal faces after cathode interior plasma interaction.

EBSD is a surface analysis technique that allows quantitative microstructural analysis in SEM up to a nanometer scale. In this method, a beam of electrons is focused at the point of interest on a tilted sample. Upon inelastic interaction between the impinging electrons and the atomic structure of the sample surface, scattered electrons form a divergent source of electrons close to the surface of the sample that contains information about the crystalline structure of the sample.

XRD is another surface analysis method that provides information about the crystalline nature of materials at penetration depth of around 10µm. Similarly to EBSD, XRD employs constructive interactions between X-rays and atomic structures producing patterns that can be recorded and used against database information to deconvolve the different phases present in the sample.

Results from different analytical approaches collectively revealed that the observed work function reduction is likely due to the emergence of a crystallographic texture in the LaB6 insert induced by the interaction with Xe plasma. In

addition, we hypothesize that forced cationic termination may be a secondary factor contributing to the work function reduction in operating cathodes.

1.6 Impact of results

Together, this work provides an in depth insight into the thermal behavior and effect of plasma exposure on polycrystalline LaB6 inside a hollow cathode. Results

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References P. Guerrero

exposure on LaB6 suggest that the evaporation rates of LaB6 hollow cathodes may

be much lower than previously thought and therefore their lifetime much longer. Given the importance of lifetime for EP components, LaB6 could outperform

current technologies and become the component of choice in EP thrusters for future space missions.

We show that material compatibility is still an unresolved issue for LaB6.

Graphite cups around the LaB6 insert can still lead to contamination of the

thermionic emitting surface. The effect of this contamination was manifested by an increase in the insert temperature. This observation together with the temperature transients suggest that common cathode experimental practice needs to be updated in order to obtain significant value from experiments. Furthermore, the problem of material compatibility has been shown to be very detrimental for cathode lifetime and therefore, we urge a solution to be found before unexpected premature failures start occurring.

From the cathode modelling standpoint, this work demonstrates the following: assuming the cathode plasma solution is accurate, the classical model to compute thermal fluxes from the plasma solution is not accurate. In fact, we were only capable of finding a reasonable agreement with experimentally measured insert temperatures when we used a two step neutralization model for the return current of ions to the cathode. This is a major finding as the involvement of a two step neutralization process was not previously recognized. Furthermore, this modelling approach may be applicable to other low work function cathode technologies.

Our contribution to the understanding of the correct chemical picture behind the work function evolution in LaB6 emitters upon plasma exposure should also be

noted. We have shown that the only phase present after plasma exposure at room temperature is LaB6. We also prove that a crystallographic texture appears after

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BIBLIOGRAPHY

[1] John R. Brophy, Marc D. Rayman, and Betina Pavri. “Dawn: An Ion-Propelled Journey to the Beginning of the Solar System”. In: 2008 IEEE Aerospace Conference. IEEE, Mar. 2008, pp. 1–10._doi:10.1109/AERO.2008. 4526264 (cit. on p. 2).

[2] E. Y. Choueiri. “A Critical History of Electric Propulsion: The First 50 Years (1906-1956)”. In: Journal of Propulsion and Power 20.2 (Mar. 2004), pp. 193–203.doi:10.2514/1.9245 (cit. on p. 3).

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[4] Dan M Goebel et al. “Hollow cathode theory and experiment. I . Plasma characterization using fast miniature scanning probes”. In:Journal of Applied Physics 98.11 (2005), p. 113302. _doi: 10.1063/1.2135417 (cit. on pp. 5, 13).

[5] Torsten Lundstrom. “Borides: Solid-State Chemistry”. In: Encyclopedia of Inorganic Chemistry. Chichester, UK: John Wiley & Sons, Ltd, Mar. 2006.

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[6] J. M. Lafferty. “Boride Cathodes”. In:Journal of Applied Physics 22.3 (Mar. 1951), pp. 299–309. doi: 10.1063/1.1699946 (cit. on pp. 6, 8, 10).

[7] A. M. Alper.Phase Diagrams. Elsevier, 1976, pp. 91/159, 142/3. _doi: 10. 1016/B978-0-12-053204-9.X5001-2 (cit. on p. 7).

[8] Chun-hua Chen et al. “Structural refinement and thermal expansion of hexaborides”. In: 366 (2004), pp. 2003–2005.doi:10.1016/S0925-8388(03) 00735-7 (cit. on p. 7).

[9] Koichi Momma and Fujio Izumi. “VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data”. In:Journal of Applied Crystallography 44.6 (Dec. 2011), pp. 1272–1276.doi:10.1107/S0021889811038970(cit. on p. 7).

[10] Alexander Dean Elliot. “Structure of pyrrhotite 5 C (Fe 9 S 10 )”. In: Acta Crystallographica Section B Structural Science 66.3 (June 2010), pp. 271–279.

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[11] M. E. Schlesinger, P. K. Liao, and K. E. Spear. “The B-La (Boron-lanthanum) system”. In: Journal of Phase Equilibria 20.1 (1999), pp. 73–78. _doi: 10. 1361/105497199770335974 (cit. on p. 8).

[12] Longuet-Higgins. “The electronic structure of the borides M B 6”. In:Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 224.1158 (July 1954), pp. 336–347. doi: 10.1098/rspa.1954.0162(cit. on p. 8).

[13] Barbara Albert and Harald Hillebrecht. “Boron: Elementary Challenge for Experimenters and Theoreticians”. In: Angewandte Chemie International Edition 48.46 (Nov. 2009), pp. 8640–8668. _doi: 10.1002/anie.200903246 (cit. on p. 8).

[14] R. A. Andrievski Y. G. Gogotsi. Materials Science of Carbides, Nitrides and Borides. Vol. 68. 1999. _doi: 10.1007/978-94-011-4562-6 (cit. on p. 8).

[15] M Gesley and L.W. Swanson. “A determination of the low work function planes of LaB6”. In:Surface Science 146.2-3 (Nov. 1984), pp. 583–599._doi: 10.1016/0039-6028(84)90451-5 (cit. on p. 8).

[16] Michael Trenary. “Surface science studies of metal hexaborides”. In: Science and Technology of Advanced Materials 13.2 (Apr. 2012), p. 023002. _doi: 10.1088/1468-6996/13/2/023002 (cit. on pp. 9, 10, 11).

[17] Jian Wang et al. “Work functions of metal hexaborides: Density functional study”. In:Modern Physics Letters B 32.2 (2018), pp. 1–8._doi: 10.1142/ S0217984918500070 (cit. on pp. 9, 10).

[18] S.A. Chambers et al. “Cesium and oxygen coadsorption on LaB6, single crystal surfaces”. In: Surface Science 118.1-2 (June 1982), pp. 75–92. _doi: 10.1016/0039-6028(82)90015-2 (cit. on p. 9).

[19] Johannes Voss et al. “Thermionic current densities from first principles”. In: Journal of Chemical Physics 138.20 (2013). _doi: 10.1063/1.4805002 (cit. on p. 9).

[20] M A Uijttewaal, G. A. de Wijs, and R. A. de Groot. “Ab Initio and Work Function and Surface Energy Anisotropy of LaB 6”. In: The Journal of Physical Chemistry B 110.37 (Sept. 2006), pp. 18459–18465. _doi: 10.1021/ jp063347i (cit. on pp. 9, 10, 16).

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[22] Ioannis G Mikellides et al. “Hollow cathode theory and experiment. II . A two-dimensional theoretical model of the emitter region”. In: JOURNAL OF APPLIED PHYSICS (2005), pp. 1–14. _doi: 10.1063/1.2135409 (cit. on p. 13).

[23] Ioannis G Mikellides et al. “Plasma processes inside dispenser hollow cathodes”. In:Physics of Plasmas 13.May (2006), p. 063504. _doi: 10.1063/1.2208292 (cit. on p. 13).

[24] Ioannis G Mikellides et al. “Wear Mechanisms in Electron Sources for Ion Propulsion , II: Discharge Hollow Cathode”. In: Journal of Propulsion and Power 24.4 (2008)._doi:10.2514/1.33462 (cit. on p. 13).

[25] Ioannis G Mikellides et al. “The discharge plasma in ion engine neutralizers : Numerical simulations and comparisons with laboratory data”. In:Journal of Applied Physics (2010), pp. 1–12. _doi: 10.1063/1.3514560 (cit. on p. 13).

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C h a p t e r 2

WORK FUNCTION REDUCTION IN LANTHANUM

HEXABORIDE HOLLOW CATHODES OPERATED IN GAS

DISCHARGES

2.1 Abstract

Thermal characterization of lanthanum hexaboride (LaB6) hollow cathodes

has revealed lower than expected electron emitter temperatures when the cathode reaches steady state. This phenomenon is observed at discharge currents ranging from 5 to 35 A and xenon mass flow rates of 5 to 25 sccm in cathodes with three different orifice diameters. Thus, the accepted value of the work function for polycrystalline LaB6, 2.66 eV, does not describe well the emission characteristics

of LaB6 hollow cathodes operating with internal gas discharges at steady state.

The measured temperatures and a model of the hollow cathode emitter and xenon discharge were used to estimate the value of the work function in these experiments, yielding a value ranging from 2.1 to 2.44 eV. Measurements of the work function as a function of depth on a hollow cathode emitter using X-ray photoelectron spectroscopy and ion beam milling indicate that the work function for lanthanum-rich stoichiometry is lower than 2.66 eV. We postulate several mechanisms that could explain this enhancement. This observation has consequences on the design, study approach, and operation of these cathodes and potentially other cathodes with hollow configuration. Furthermore, it opens the question of why the work function is enhanced. Regardless of the answer to these questions, LaB6 cathodes

are now important competitors to other conventional cathode technologies.

2.2 Introduction

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employing this architecture. However, this ambitious goal is extraordinarily difficult given the large mass necessary to reach Mars and provide habitable conditions for the astronauts. A very high efficiency propulsion system such as high-power electric propulsion can yield mass reductions that enable near-term deep space missions. NASA is investing in high power, light weight solar arrays and high power Hall thruster systems to enable this vision. Reaching further with heavier payloads is the key objective of this new endeavor. In order to successfully accomplish this challenge, a new scalable propulsion system has been under development at NASA since 2012. The goal is to develop the components for an Advanced Electric Propulsion System (AEPS) with a total system power of 40 kW. A key building block of the system is the Hall Effect Rocket with Magnetic Shielding (HERMeS). Hollow cathodes are at the heart of the system, with LaB6 being one of the cathode

technologies under development.

Increased understanding of the detailed physical processes underlying Hall thruster operation has eliminated some of the possible failure modes that can limit the thruster lifetime. One example of a significant breakthrough in Hall thruster technology is the so-called magnetic shielding, a technique that employs carefully engineered magnetic fields to protect surfaces close to the plasma discharge from erosion. Nonetheless, a number of failure modes associated with different Hall thruster components are yet to be resolved, several of which are related to the thruster cathodes. It is important that the Hall thruster service life, aimed to exceed 35k hr, is not limited by the cathode lifetime. Thus, understanding cathode failure modes is of paramount importance for future NASA activities.

LaB6 hollow cathodes have a demonstrated capability for long life operation.

They also exhibit other advantages: they are more resistant to poisoning by reactive gases than dispenser cathodes and they are scalable to high discharge densities [1]. LaB6 emitter lifetime is ultimately limited by evaporation related to

high temperature operation and thermal loads.

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2.2. Introduction P. Guerrero

function φ (φ is the work function of the material with a nominal value of 2.66 eV for LaB6). The fraction of electrons in the emitter with sufficient energy to escape

the work function barrier at the surface is related to the surface temperature by Eq. 2.1. Thus, precise knowledge of the emitting surface temperature distribution is essential to fully understand the current emission capability. In addition, insert evaporation, one of the main failure modes that affects state of the art cathodes, is exponentially related to the material temperature.

The thermionic emission current density (jther) is defined by the

Richardson-Dushman equation:

jther(φ,X)= D T(X)2exp

₋_e₍φ₋φ

Schottky)

kBT(X)

(2.1)

with the parameter D= 29 A/cm2K2 correcting for the temperature dependence of the work function,T(X) is the temperature at any point X in the insert, kB is

Boltzmann constant. φSchottky is the reduction in the work function due to the

external electric field and e is the electron charge.

Precise temperature measurements are challenging due to the high temperature at which these cathodes normally operate, often close to 2000 K. Further, LaB6

cathodes consist of many components that cluster in assemblies, which makes them difficult to instrument. Previous efforts have established two approaches for measuring temperatures inside hollow cathodes, namely thermocouples and fiber optic pyrometers.

Type C commercial thermocouples have the highest operating temperature range (0-2320 °C), which makes them an attractive option for cathode instrumentation. The downside is that they typically have a 1% precision. Fiber optic systems, on the other hand, require calibration, which can be very difficult to accomplish at that high temperature without using thermocouples.

In this paper, we present the results from using type C thermocouples to measure temperatures inside LaB6cathode inserts for a variety of cathode operating

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simulations using the in-house plasma solver OrCa2D and COMSOL Multiphysics®_.

Surprisingly, the data revealed that the commonly accepted work function value for polycrystalline LaB6 (2.66 eV [2]) cannot adequately describe the emission

characteristic of the cathode at steady state. Instead, lower work functions are necessary to fit the measured temperatures and discharge currents to the Richardson-Dushman equation. We propose several mechanisms that could be responsible for these atypically low work function values, including formation of stable phase LaB4, forced cationic termination of LaB6 crystals, formation of a

crystallographic texture, and surface absorption of some contaminant that actually enhances the LaB6 work function.

2.3 Description of the measurement approach

The cathode used in these experiments has been described in [1]. Briefly, it consists of a cathode tube with a cylindrical LaB6 emitter (the “insert”) positioned

at the downstream end in front of an orifice plate, which serves to increase the internal gas pressure (Fig. 2.1). The downstream portion of the cathode tube is surrounded by a heater used to preheat the insert material for ignition. The heater is covered by tantalum foil shielding to minimize heat loss through radiation at start or during normal operation. Finally, the assembly is enclosed in one more concentric electrode, termed the keeper, which is used as an ignitor electrode or to maintain a secondary discharge to keep the cathode operating in the event of extinction of the main discharge.

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2.3. Description of the measurement approach P. Guerrero

LaB₆insert

Keeper

Orifice plate Cathode tube

Heater insulation Heater

Figure 2.1: LaB6 hollow cathode schematic.

depth, respectively (see Fig. 2.2). A second order polynomial was used to fit the three measurements to give an approximation of the temperature profile. In order to assure good thermal contact between the thermocouples and the location where temperature is measured, the thermocouples were installed using a pre-loaded spring strategy. By using this approach, each individual thermocouple can accommodate the thermal expansion of the different components of the cathode assembly and still guarantee that the bottom of the thermocouples are against the insert wells at any point in time during the experiments.

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Figure 2.2: Insert finite element model with three thermocouples wells.

measurement accuracy.

A copper cylindrical anode 50.8 mm in diameter and 25.4 cm long was placed ∼20 mm from the keeper face, concentric with the assembly. Experiments were performed inside a 4 m3_{stainless steel vacuum chamber equipped with two 25.4 cm}

diameter cryopumps which produce a base pressure of 9×10−8 Torr. Data were acquired using a custom built system based on a Opto22 SNAP-PAC-EB brain that measures voltages, currents, and xenon mass flow rates with precision of 10 mV, 10 mA and 0.01 sccm with respect to calibrated values, respectively, and a 2 s refresh rate. Thermocouple signals were also acquired with the aforementioned equipment, which performs the cold junction temperature correction.

2.4 Experimental Results

We initially sought to acquire the temperature distribution using the three thermocouple approach described above. When the cathode was set to a specific operating condition, a temperature transient was observed before the temperatures stabilized. Interestingly, we found that the duration of the transient is longer than expected and depends on the previous history of the cathode: if the cathode is in steady state and a small change to either the discharge current, JD, or the xenon

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2.4. Experimental Results P. Guerrero

a few tens of degrees of overshoot or undershoot with respect to the steady state temperature. In such cases, the duration of the transient is around 30 min to a few hours. A detailed description of the transient behavior is provided in the following section.

Due to the variation in the time required to reach steady state and the large number of operating points to be tested, we developed a data acquisition and control (DAQ) strategy which autonomously determines when the cathode reaches steady state. The system defines steady state as the point where the temperature difference in two consecutive 15 min intervals is less than 1 °C for all three thermocouples.

2.4.1 Transient behavior

2.4.1.1 Initial start with a new LaB₆ insert

Using the automatic DAQ setup described above, we first assessed the system behavior upon initial start with a new LaB6 insert. The ignition was performed at

JD =25A and mÛXe= 14.75sccm. Data showed that for a new insert, it takes tens

of hours to reach steady state (Fig. 2.3). After that long transient, we observed a small amplitude, low frequency periodic fluctuation in the measured temperatures (although this phenomenon is not fully resolved in Fig. 2.3).

In addition, the data showed a peak temperature of 1737 °C and that the condition ∆Tmean

∆t =0 occurred around 65 hr after ignition, whereTmean is the mean temperature of all three thermocouples.

2.4.1.2 Initial start after atmospheric exposure

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0 20 40 60 80 100 120 140 Time, h

0 500 1000 1500 2000

Temperature,

° C

-2 -1.5 -1 -0.5 0 0.5 1 New insert temperature transient

74 76 78 80 82

Time, min 1400

1600 1800

T,

° C

Transient at start

1737 °C 1194-1292 _°C

Figure 2.3: Thermal transient for a new insert at JD=25A and mÛXe =14.75sccm

with the nominal orifice. In the inset it is shown the details of the temperature transient during the first few minutes of operation after the discharge power supply has been enabled.

reignited the cathode with JD = 25 A and mÛXe = 14.75 sccm. This reignition

operation was performed manually, therefore, the temperature right before ignition is not the same for the three cases shown in Fig. 2.4. Only TC1 is shown for each start, which typically is the hottest of all three at ignition.

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-0.5 0 0.5 1 1.5 2 2.5

Time, min 1100

1200 1300 1400 1500

Temperature,

° C

Cathode ignition after atmospheric exposure

TC 1, ignition at 1279 ° C TC 1, ignition at 1244 ° C TC 1, ignition at 1208 ° C T

max= 1506 °C

T

max= 1485 °C

T_max= 1459 °C

Figure 2.4: Thermal transient at JD=25 A and mÛXe =13sccm with the nominal

orifice after exposing the cathode to the atmosphere for several hours.

2.4.1.3 Transients associated with hot reignitions

We define hot reignition as the process of igniting the cathode after a sudden shutdown (JD =0 A), and allowing only a few hundred degrees cool-down before

reigniting it. At that point, switching on only the keeper or the keeper and the heater might be necessary to reignite the cathode. Fig. 2.5 shows the temperature evolution during two different hot reignition experiments, synchronized at Time= 0 min.

Before shutting down the cathode, neither of the experiments had reached steady state, i.e., there is a temperature difference of 26 °C (Fig. 2.5). Both experiments were performed with the nominal orifice plate and JD = 25 A and

Û

mXe= 13sccm.

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-15 -10 -5 0 5 10 15 Time, min

900 1000 1100 1200 1300 1400 1500

Temperature,

° C

Cathode hot re-ignition

TC 1, experiment 1 TC 2, experiment 1 TC 3, experiment 1 TC 1, experiment 2 TC 2, experiment 2 TC 3, experiment 2

T_max= 1447 °C

T_max= 1410 °C T_min= 1229 °C

T_min= 1195 °C

T_min= 864 °C

Figure 2.5: Thermal transient associated with hot reignition at JD = 25 A and

Û

mXe = 13 sccm with the nominal orifice. TC1 temperature shown for both

experiments.

864 °C right before reignition, and the cathode peak TC1 temperature measured 1447 °C.

2.4.1.4 Transients associated with discharge current step events

Finally, we tested the cathode behavior with discharge current step events. To this end, we first ignited the cathode and allowed it to reach steady state, as determined by the DAQ system. At that point small changes in JD of 2.5 A were suddenly

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0 1 2 3 4 5

Time, h 1100

1150 1200 1250 1300 1350

Temperature,

° C

0 10 20 30 40

Temperature evolution as J

D changes

15A

Figure 2.6: Thermal transient evolution with JD at mÛXe=10 sccm with nominal

orifice.

at others there was an undershoot (between 15 A to 17.5 A and 17.5 A to 20 A). There is one case in which the temperature transitions with no over- or undershoot (12.5 A to 15 A), right in the middle of overshoot and undershoot trends.

2.4.1.5 Sudden change of steady state for one operating condition

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0 0.2 0.4 0.6 0.8 1

Time, h

600 800 1000 1200 1400 1600

Temperature,

° C

0 20 40 60 80

Contamination thermal effect

1208-1303 °C 1294-1390 °C

Figure 2.7: Abnormal thermal transient after a hot reignition with the nominal orifice at JD=25 A and mÛXe=14.75sccm.

significantly impacts evaporation, and consequently the lifetime of the cathode, we suggest that graphite deposition has an important negative impact in the service life of the cathode. Our results strongly suggest that downstream graphite cups should be eliminated or at least redesigned in future cathode designs.

2.4.2 Steady state temperatures

The steady state temperature distribution of the cathode insert was obtained for each orifice diameter at discharge currents of 5, 10, 15, 20, 25, 30, and 35 A, and for each discharge current, mÛXe was set at 5, 10, 15, 20 and 25 sccm. For the

large orifice, the 5 A case was not studied as the cathode was in plume mode for that condition over the whole mÛXe range under consideration. Temperature maps

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2.5. Discussion P. Guerrero

Figure 2.8: Detail of the contaminant deposited on the inside of the insert.

2.5 Discussion

2.5.1 Effect of orifice size on temperature

In order to assess which orifice configuration offers the best performance, we estimated the temperature profiles along the insert by fitting the data with a second degree polynomial (Fig. 2.10). For each orifice plate and cathode operating point, a different temperature profile is obtained. As minimizing LaB6evaporation is critical

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Figure

2.9:

Steady

state

temp

erature

dis

tribution

for

eac

h

catho

de

configuration

and

eac

h

thermo

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given discharge current. The profiles for discharge current above JD= 15A have

the smallest difference between maximum and minimum temperatures for any given profile. Minimizing the temperature gradient along the axis of the insert is desirable because the insert should then erode more uniformly over thousands of hours. Nonetheless, this is a consideration of lesser importance compared to minimizing the peak temperature for the same discharge current.

On the other hand, the small orifice shows the biggest temperature range over the same operating condition space. Peak temperatures are lower than for the large orifice case, but higher than for the nominal orifice size for discharge currents above 5 A. Differences between maximum and minimum temperatures along the insert are the largest of the three configurations for all discharge currents above 5 A.

The nominal orifice diameter offers the lowest temperature peaks for discharge currents above 5 A and differences between maximum and minimum temperatures that lie between those of the larger and smaller orifices. This configuration is the most appealing one in terms of thermal distribution. In this analysis, the evolution of the insert inner diameter and consequent effect on the temperature profile has not been taken into consideration when choosing the best configuration for the lifetime of the insert. That analysis would require knowledge of how the temperature profile evolves as the LaB6 insert erodes.

2.5.2 Cathode temperature sensitivity to effective emissive area

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0.2

0.4

0.6

0.8

Distance along insert / Length of insert

1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 _Temperature, ° C 0.2 0.4 0.6 0.8

1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 0.2 0.4 0.6 0.8

1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

5 A 10 A 15 A 20 A 25 A 30 A 35 A 5 sccm 10 sccm 15 sccm 20 sccm 25 sccm

0

0.5

1

Extrapolated temperature profiles along the insert

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

A / A N -250

-200 -150 -100 -50 0 50 100 150 200

250 Cathode effective emitting area sensitivity analysis

25 = J

D

=

A

D

T

2

exp(e / K

B

T

)

= 2.67 eV = 2.1 eV

Figure 2.11: Cathode effective emitting area sensitivity analysis. A is the effective area used in the Richardson equation, AN is the nominal emitting area based on

the diameter of the emitter.

expected reduction of temperature in this case is no more than 70 °C. In the case of the nominal orifice plate in Fig. 2.10, the observed reduction is on the order of 300 °C. A 300 °C temperature reduction corresponds to more than 20-fold increase in the effective emissive insert area. Even though we cannot rule out increased effective emissive area of the insert as a contributing factor, it cannot explain the magnitude of temperature reduction of the cathode at steady state observed.

2.5.3 Inferred work function

At every point on the insert emitting surface (S), the balance between the flux

Plasma Surface Interactions in LaB₆ Hollow Cathodes with Internal Xe Gas Discharge